Title:
A Strange Wilderness – The Lives of the Great Mathematicians
Author:
Amir D Aczel
Publisher:
Sterling New York, 2011 (First)
ISBN:
9781402785849
Pages:
284
Some
people among us don’t relish the prospect of studying mathematics. The probable
reason for this aversion is mostly improper assimilation of fundamentals caused
due to lapses in the method of teachers who taught them in primary schools.
Such people opt for the inexact sciences like biology or humanities like
history when the time comes to make a choice. However, reading about the
development of mathematics and the lives of its pioneers is as exciting and
satisfying as any. So, this book will be interesting for both math-philes and
math-phobes equally. Man innately possesses the ability to compute with simple
numbers. Research states that even birds do retain a basic sense of number! The
origins of mathematics was surely associated with counting, as those early
settlers on the fertile river valleys of Nile and Euphrates-Tigris used them to
keep account of their livestock. Gradually, other applications developed, like
keeping track of the seasons by counting elapsed days. Early astronomers used
it extensively to predict the sowing time. As time went on, mathematics became
more complex and began to be applied to all aspects of life. An amusing example
of a peculiar rule of marriage among the aborigines of New Guinea presented in
the book shows that mathematics can be extended to human relations as well.
Amir D Aczel has produced nearly a dozen books on science and mathematics. He
lives in the United States and contributes to newspapers and television also.
In this nice book, he tells the story of mathematics developing from humble
origins to what it is today – touching the everyday lives of all civilized
societies in numerous ways. Some books on the mechanism of human brain state
that the faculty of language and mathematics will not be developed
simultaneously in people. However, this book presents several mathematicians
who were adept at both. This pleasantly readable work is a must-have for
students of mathematics.
The
first two parts of the book neatly sums up the work done by ancient scholars in
Egypt, Greece, India, China and the Arab world. Contrary to our expectation, intellectuals
in the ancient period also traveled far and wide in search of knowledge. We
read about Greek scholars visiting Babylon and Egypt to partake of the
knowledge amassed in these cradles of civilization. Thales of Miletus was
inspired to formulate the first theorem of mathematics on a visit to the Great
Pyramid of Cheops in the 6th century BCE. Anxious to find the height
of the pyramid, he devised an ingenious way by measuring the length of the
shadow cast by the structure, which is still intriguing. Restriction of
knowledge to the initiates alone had begun in those times in the case of
Pythagoras and his disciples, who were very particular in keeping the word to
themselves and even going as far as to kill some of their brethren who wanted
to spread the message on the existence of irrational numbers which challenged
their own intellectual foundations. Aczel gives a fitting representation of
Indian thought guided by Aryabhata and Vishnugupta. Though he remarks that the
contributions of these masters may have been guided by assimilation of Greek
thought diffused through increased trade between the two countries, he has been
straightforward in assigning the invention of algebraic and trigonometric ideas
to India. Greece excelled in geometry. When the classical age ended in Greece
and Alexandria, the beacon of learning passed to the Arabs who kept it lit till
Renaissance, when it was handed over to Europe. Combining elements from Greece
and India and producing original thought of their own, Arab mathematicians
founded the roots of some of the branches of modern mathematics. The term
algebra derives its etymology from a treatise called ‘Al Gabr Wa’l Muqabala’ by Muhammad ibn Musa al-Khwarizmi who lived
in the court of caliph al-Mamun. Signs of influence of Brahmagupta’s work
‘Brahmasphuta Siddhanta’ are said to be unmistakable in al-Khwarizmi’s work
(p.46). With Jamshid al-Kashi (1380 – 1429), Arab scholarship faded into
oblivion. Arabs translated ancient Greek manuscripts and Indian numerical
notation to Arabic, which was translated to Latin in the Middle Ages, which
helped Renaissance science to flourish. The book also sets aside a chapter on
Chinese origins of mathematical concepts.
The seventeenth century CE may be
credited with the honour of the origin and development of modern mathematics.
Descartes, Newton and Leibniz shone with meridian splendour in this period,
among an impressive array of scholars. The sharp disparity between England and
continental countries like Germany are seen here. While in England it was
possible for a talented man to find avenues for further study and research such
as Cambridge and Oxford, without worrying too much about the financial
circumstances of leading their daily lives, in Germany and other countries, the
scholar had had to apply for patronage to a feudal lord or leading members of
the clergy. Naturally, such a system was vulnerable to the fortunes of the
patron in a battle or to the loss of favour of the patron himself with the
king. Wherever there was a stable government, scholarship flourished. France
led the field till the beginning of the nineteenth century on account of this,
while Germany was splintered among a plethora of weak city states. After the
downfall of Napoleon and amid the unsettled political turmoil which followed
it, France lost its position it had enjoyed with the work of Laplace, Legendre,
Galois, d’Alembert and Lagrange. Germany, consolidated in this century on the
political front, and its repercussions were seen in mathematics as well, with
the advent of notable personalities like Cantor, Dedekind, Weierstrass and
others. We note another noteworthy fact in this regard. Many mathematicians in
the Renaissance era were devout Christians, Newton being the most prominent.
Mathematicians’ personal beliefs inevitably seeped into their work too. Newton
studied the solar system in light of gravitational forces exerted by the bodies
in orbit and reached the conclusion that it is stable in the long term due to
God’s intervention. Laplace, an atheist who studied the same problem in a
Europe conditioned by Enlightenment, declared boastfully that the stability of
the solar system is not in need of the god hypothesis. As can be expected, he
also reached the conclusion that the solar system is stable.
When we reach the modern period,
mathematics has grown complex and out of reach of common people. No fundamental
advance has taken place in the last 150 years, except perhaps the impetus made
in non-Euclidean geometry by the development of Einstein’s theory of
relativity. Researchers studied some of the highly specialized attributes of a
theory, aloof from the buzzle of the street and away from any concern to find
an application for the theory. Practitioners of pure mathematics take pride in
the fact that the extreme abstractness of their field precludes the necessity
to look for a practical way to employ the theory. When no path breaking
advances were forthcoming, mediocrity set in. Even though Aczel praises the
effort of Nicolaus Bourbaki, a group of maverick mathematicians posing as an
individual, and Alexander Grothendieck, readers get a feel that instead of
pioneering new ways, they have gone in search of cheap popularity tricks and
pranks. Grothendieck was a researcher who suddenly turned to politics and environmentalism
and effaced himself from public view by hiding somewhere in the Pyrenees. In an
act of sheer irresponsibility, he burnt all his contributions to mathematics in
addition to taking all electronic content off the Internet. Aczel revers this man,
but readers believe that he is an impostor.
The text is very easy to read through,
presented in a concise but effective way. All the usual anecdotes and events
are included, but the book doesn’t advance any original ideas except the flawed
one on the greatness of Grothendieck. There are no exclusive information
available in this book, which is unattainable from others. Lot of photographs
and paintings are included, along with a good index. The bibliography is
extensive. However, the narration abruptly ends, without a proper epilogue or
musing about the future course of mathematics. In this vein, it may be thought
of as a description without insight or any contribution from the author apart
from compiling data about various mathematicians. However, the author gives a
respectable mention of Indian masters of old and new, and wholeheartedly
acknowledges their pioneering roles. A number of sidebars are provided, but
they blend confusingly with the text as the layout doesn’t neatly separate them
from the main text.
The book is recommended.
Rating: 3 Star
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